*by Valerio Sabelli*

In the sight of occasional investors, the equation “very rare event = impossible event” is often applied.

However, those who invest heavily in their portfolios increasingly need – especially after catastrophic events such as the American subprime mortgage real estate bubble in 2006 – a **tail risk analysis** and countermeasures aimed at limiting damage in case of rare, but possible, events.

So, let’s delve into **tail risk** and find out what is the most used strategy to minimize damage in case of **tail event**.

## What is tail risk

Traditional strategies for building a portfolio are based on the idea that the probabilities of obtaining profits and losses follows a normal distribution (namely that the probability of having extremely low or extremely high revenues is close to zero). The truth is that is not the case: in order to reflect the fact that these distributions have “fat tails”, in other words that even the **odds of extreme losses/gains** are not zero, the **tail risk** is calculated.

To understand what tail risk is, it is first necessary to define what a tail event is: it is an **event that can occur with a very low probability**, but which – if this were to happen –might have **severe consequences on economic and financial markets**. This event causes such high **volatility** precisely because a small number of traders have been able to predict it.

Obviously, just as it is difficult to predict the event, it is also **complicated to estimate the risk for investors**, by virtue of the uniqueness of each event of this type and the correlations created between the various investments (despite the diversification strategies that we may have put into action).

## How to calculate and mitigate tail risk

As previously said, tail events not happen frequently and their impact is different with each new occurrence.

The measure used to understand the effect of these events is the **Expected tail loss** (**ETL**). This is an extension of the so-called VaR (Value at Risk) statistic, which is a threshold statistic defined as the minimum amount of portfolio loss at a specified probability and horizon. For example, hypothetical portfolio might have a 5% VaR value of one million euro. This means that 5% of the time the portfolio will lose that amount of money in a specified time horizon, say over a month. However, we have no indication of how much we would lose if we exceed the millions of euro mentioned above.

ETL is calculated by averaging the losses that are beyond a certain threshold of a portfolio return distribution. There are many ways to create the distribution, but the simplest is to use the *empirical portfolio returns*, ergo real measured results.

As a consequence, **thanks to a weight optimization operation between the assets in the portfolio, we can find the combination of investments** that minimizes ETL. Another alternative way of esteeming are the *random walks* (also used in physics to simulate random “deviations” from the starting trend of real data) or *Monte Carlo simulations* (based on the calculation of linear regressions that estimate the values of the assets through experimental averages).

As in other use-cases relating to big data, also here it is possible to find various data sources and software on the market that help us in these calculations, suggesting the right strategies to be adopted.

So, how can we protect ourselves from these events? We can take advantage of the so-called **risk hedging strategies**. The idea is to “spend” part of the revenues each year to “buy” protection against market alteration.

To get an idea of how it works, we can draw a parallel with an example related to everyday life. As an example, suppose you have just bought a very expensive house. It could happen – albeit with a very low probability – that our house is destroyed by a fire. In order to mitigate the damage, in case this happens, we purchase a home insurance which, in fact, “bets” on that event. We therefore accept to lose the insurance premium every month, trying to cushion the “economic disaster” that we would endure with the fire. Therefore, having a **hedging** mechanism that can protect us in the case of a tail event corresponds to **use financial instruments or market strategies in order to reduce the risk of significant economic losses**, accepting a slightly smaller profit in everyday business.